Industry: Retail Product: ModelRisk Application: Analyzing Seasonal Trends and Demand Uncertainty
Merchandising commits holiday-category stock to land in weeks 46–49 because the fitted seasonal index says demand peaks in week 48. The fitted index is a single curve. The real season is not. Simulate 40,000 plausible season shapes in ModelRisk and the peak week is a distribution — P10 week 46, median week 48, P90 week 50, a standard deviation of 1.5 weeks — and the probability the peak lands outside the planned buy window is 21%, almost all of it (16%) arriving late. Stock that lands four weeks before a late peak sits on the floor through the wrong fortnight.
This is not a forecasting-accuracy problem and it is not a promotion. It is the uncertainty in the shape of the recurring seasonal pattern itself — when the peak comes and how sharp it is — and the inventory risk of buying to the wrong week.
The deterministic approach fits one seasonal index per week from history and treats it as fixed. We instead generate a full season every trial, holding two properties that a real seasonal profile must satisfy: the 52 weekly indices average to 1.0 (an internally consistent profile, no negatives), and the weeks move together rather than independently.
Because the shift and amplitude are single per-year draws applied to the whole curve, the weeks are correlated by construction. The realised correlation between two off-peak weeks (week 40 and week 44) across trials is +0.84 — strongly positive, confirming the season moves as a coherent shape rather than 52 independent noises that would average away. That shared structure is the entire source of peak-timing risk.
The fan chart shows the P10–P90 band of the seasonal index across all 52 weeks. The deterministic profile (dashed) is one smooth curve through the middle; the simulated band reveals both the lateral spread of the peak and how much higher a sharp year can spike. A single fitted index understates peak sharpness precisely because smoothing averages over the very years the buyer most needs to plan for.
The deterministic plan says one word — week 48 — and sizes the buy window around it. The simulation says the peak is a distribution with real mass on either side of the plan.
Against the shaded weeks-46–49 buy window, the peak-week histogram shows P10 week 46, median week 48, P90 week 50. The 21% that falls outside splits 16% late, 5% early — the asymmetry matters because a late peak is the expensive failure mode: stock that arrived on schedule is already aging when demand finally crests. The deterministic "week 48" is the mode, but planning to the mode ignores the one-in-five seasons that miss it.
Knowing the peak is uncertain only matters if it changes the buy. It does. If replenishment stock lands in week k and sells over the following four weeks, the share of peak-season demand actually captured depends sharply on k — averaged across all simulated seasons.
Landing in week 47 captures 95% of achievable peak-season demand; the planned window (weeks 46–49) captures 95% down to 83% as you slide later within it. But the curve is brutally asymmetric on the far side: land in week 50 and capture collapses to 59%; week 52 captures just 17%. Being two weeks early costs a few points; being four weeks late costs more than half the season. That asymmetry is the argument for buying to land slightly ahead of the modeled peak and holding flexible replenishment, rather than committing everything to a single week.
The season-shift common factor dominates peak-timing uncertainty (±2.5 weeks), well ahead of weather-onset timing and calendar drift. Amplitude and width multipliers reshape the peak's height but barely move its week. The lesson for data collection: a tighter read on what slides the whole season — weather onset, holiday-calendar position — narrows the timing risk far more than refining the peak's magnitude.
A fitted seasonal curve tells you when the peak usually is; only the distribution of curves tells you the one-in-five chance it arrives when your stock is already on the clearance rack.